Project image on uv sphere (for pool balls)
Using the Cycles Render Engine.

Create a UV Sphere > Shift +”A” > Choose “Mesh” > “Sphere” from the drop down menu.

While still in Object Mode > Shading > Smooth from the Tool Bar (Press “T” to toggle it on/off). Also press CTRL + “A” and apply the Scale. (You can also add a Subdivision Surface Modifier).



In the Materials Tab create a new material.

In the Node Editor create your node set up. Including your image texture with an Alpha channel. I used a .PNG with an alpha channel image file.



EDIT:
I realized the the stripe (purple area)did not have any gloss so I've added an additional node set up for that.

Also I took out some roughness in the Gloss Nodes / Added  slight blur to the Image Texture / Added a slight bit of yellow and red to the white part of the ball.

Go into UV Editing Mode press TAB to go into Edit Mode and select all > Press “U” and select “Sphere Projection” from the drop down menu.

Select “Texture” and you will be able to see a preview of your texture. 



If the texture is stretched while still in edit mode and your cursor in the UV Editing window adjust the “X” scale of the UV Map scale by pressing “S” then “X”.



In this example in order to avoid a gap in the image texture on the back of the Sphere > in the Image Editor scale the UV Map down to fit the Texture.